It was after a trip to London that Joseph Einhorn decided to name his website Fancy.com, a nod to digging something—a rather British turn on the ubiquitous Internet act of "liking" an item. The crowd-curated site reads a little like Pinterest, with one major difference: buying power.

"When we started, we just linked out, like other sites," Mr. Einhorn said. "But people kept pushing to be able to put it all in a cart and buy it right there."

Mr. Einhorn obliged. Fancy.com ships merchandise from any site to anywhere in the world, and provides same-day delivery in 100 cities, including 40 outside the U.S. "In 2014, our goal is figuring out what people want and getting it to them faster than anyone else," said Mr. Einhorn.

Fancy.com appeals to what the native of Manhattan calls leading-edge shoppers. High-end goods, a sleek aesthetic, convenience and still uncommon features like a Google Glass shopping app and acceptance of Bitcoin are pushing Fancy.com sales higher, and keeping Mr. Einhorn busy.

"I came across the Fancy app and I liked it," said Ed Gilligan, American Express Co. president and a Fancy.com board member. "It's upscale and edgy. I was a user even before we were an investor."

Mr. Einhorn, a father of two who started his career at Capital IQ at age 16, calls Fancy "my dream project. It's a combination of my personal interests in design and culture and my experience in big data."